‘Elvis & Nixon’: An odd picture about ... an odd picture

The most requested photo from the National Archives and Records Administration shows two men shaking hands.

The man on the left wears a tiny U.S. flag pin on his lapel; it goes with the row of flags behind them. He smiles warily, like a business partner who suspects he’s about to be swindled. The man on the right wears the kind of belt favored by pro wrestlers; it goes with the bric-a-brac on the wall shelves. His expression suggests glazed indifference.

This was the 1970 meeting of The King and the President, Elvis Presley and Richard Nixon. The new movie “Elvis & Nixon” offers an entertaining meditation on the how and the why leading up to this famously strange photo.

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The briefly married team of Joey and Hanala Sagal wrote the script with Cary Elwes – yes, the “Saw” actor – and they stick closely to published history where it’s known.

Elvis (Michael Shannon) stops by the northwest gate of the White House with a five-page letter on American Airlines stationery. He’s accompanied by handler Jerry Schilling (Alex Pettyfer), who’s vaguely trying to break away from his boss. Presley proposes to work as a Federal Agent at Large and combat the drug subculture ruining the youth of America; the oddity of this request will not be lost on anyone who knows Presley abused prescription drugs.

Nixon aide Bud Krogh (Colin Hanks) figures Presley is still idolized by voters young and old – unlikely in 1970, but such an unhip drone might not have known that. So Nixon (Kevin Spacey) reluctantly agrees to a meeting and, to his surprise, likes the guy who tries to bring guns into the Oval Office and swipes the presidential M&Ms. They agree about society (rotten), the media (prying), young people (getting worse) and Communists (always a shadowy threat).

Director Liza Johnson keeps us in the right period in the usual ways – hairstyles, music, clothes, cars – but also captures the anxiety that hovered over America during the Civil Rights Era. When Elvis’ black chauffeur takes him to a doughnut shop with no white customers, we’re not sure what will happen. Are the patrons genuinely admiring, mocking or about to turn violent? (Elvis unfairly acquired an early reputation for racism, though Jet magazine debunked it.)

Spacey goes for verisimilitude: Nixon’s hunched and defensive body language, his anxious eyes, his gruff “good fella” voice. Shannon aims for a more generalized impression of the enigmatic, personable but guarded superstar.

Yet both convey a deep weariness at having been in the public eye so long, and both characters come across as introverts who never felt loved or admired for all they’d given their country. Within seven years, one would be publicly disgraced and the other dead. But for this strange moment in history, they belonged together.